Mathematical things I have toyed with.

Last Up date: 2017 April 15 on nuMacMini: work/gd/lafarr/math
Recent changes: Moved to nuMacMini from iMac
Started on: Sat 2004-03-20 Page redone: 2011 January 14

There are many definitions of Mathematics. For many it is about arithmetic. For me, it is about getting correct answers with as little arithmetic as possible. Yes, it starts with counting and goes on from there.

We count in a number system created by the convenience of using our fingers on both hands. But, because ten is not dividable by three there are many examples where, for convenience, we do not use base ten. Most notable examples are: Time, and Angles where the basic unit: a full circle of the planet we live on is broken up into a number of pieces that is divisible by three. Other examples are: the dozen, feet & inches, and keys in a music octave.

It is unfortunate that God did not give us another thumb on each hand, mathematically six is a much better number than five, then we would have had twelve fingers, and counted base twelve instead of ten. He did wise-up and gave insects 6 legs! (A 5 legged criter would be stupid.)

Click here for more on this fantasy of changing the number system we use to be base twelve. I agree it would have many advantages, but when we can't in the USA get people to change to Metric; think how difficult it would be to change the base of the number system. We can't even change the stupid way many words are spelled in English. Tradition is a curse on human thinking.

Things I have written about: Some of the pages are old, and some links may not work.

  • My Random Number Generation and Encryption/Decription program useing it.
  • Selected integer solutions for: x2 + y2 = z2 A more complete list is here.
  • √‾2 in 100 "best" fractions.
  • My description of calculating the number of possible BINGO Cards.
  • I have updated an old prime number generation program, to use my favorite assembler.
    I was interested in the number of prime twins occurred in a large table of prime numbers.
  • If you just want every 50,000th prime from 611,957 up to 302,569,483 I have them here.
    Following are links to earlier pages I thought might be interesting. They are in the order I generated them:
  • Description of DOS programs I have written (Command line Executable under Windows) to do arithmetic things you might find interesting or useful.
  • My explanation of the Euclidian Algorithm and Continued Fractions.
  • Description of the Lehmer Chain machine displayed at the Computer History Museum.
  • My attempts at making a working Chain Machine.
  • My notes for a talk about Congruence Arithmetic. Unfortunately, too much is left out to make it understandable without my live explanations and examples.

Here are some links I think are interesting.

  1. has great graphics and explanations for a lot of different subjects. I think the fellow is German, because he has much of his pages in German & English.
  2. lots of intersting links, including one on FFT based multiplication of large numbers.

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